Empirical Rule & Z-Scores

Front

What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

What is a Z-score?

Back

A Z-score indicates how many standard deviations a data point is from the mean of a distribution.

Front

How do you calculate a Z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What percentage of data falls between z = -1 and z = 1 in a normal distribution?

Back

Approximately 68% of the data falls between z = -1 and z = 1.

Front

What does a Z-score of 0 represent?

Back

A Z-score of 0 indicates that the data point is exactly at the mean of the distribution.

Front

If a Z-score is positive, what does it indicate?

Back

A positive Z-score indicates that the data point is above the mean.

Front

If a Z-score is negative, what does it indicate?

Back

A negative Z-score indicates that the data point is below the mean.

Front

What is the area under the normal curve to the left of z = 1.33?

Back

Approximately 90.82% of the data falls to the left of z = 1.33.

Front

What is the 95th percentile in a normal distribution?

Back

The 95th percentile is the value below which 95% of the data falls.

Front

How do you find the percentile rank of a score?

Back

To find the percentile rank, calculate the percentage of scores that fall below the given score.